Proof of Theorem ps-1
Step | Hyp | Ref
| Expression |
1 | | oveq1 6657 |
. . . . . 6
|
2 | 1 | breq2d 4665 |
. . . . 5
|
3 | 1 | eqeq2d 2632 |
. . . . 5
|
4 | 2, 3 | imbi12d 334 |
. . . 4
|
5 | 4 | eqcoms 2630 |
. . 3
|
6 | | simp3 1063 |
. . . . . . . . 9
|
7 | | simp1 1061 |
. . . . . . . . . . . 12
|
8 | | simp21 1094 |
. . . . . . . . . . . 12
|
9 | | simp3l 1089 |
. . . . . . . . . . . 12
|
10 | | ps1.j |
. . . . . . . . . . . . 13
|
11 | | ps1.a |
. . . . . . . . . . . . 13
|
12 | 10, 11 | hlatjcom 34654 |
. . . . . . . . . . . 12
|
13 | 7, 8, 9, 12 | syl3anc 1326 |
. . . . . . . . . . 11
|
14 | 13 | 3ad2ant1 1082 |
. . . . . . . . . 10
|
15 | | hllat 34650 |
. . . . . . . . . . . . . . . 16
|
16 | 15 | 3ad2ant1 1082 |
. . . . . . . . . . . . . . 15
|
17 | | eqid 2622 |
. . . . . . . . . . . . . . . . 17
|
18 | 17, 11 | atbase 34576 |
. . . . . . . . . . . . . . . 16
|
19 | 8, 18 | syl 17 |
. . . . . . . . . . . . . . 15
|
20 | | simp22 1095 |
. . . . . . . . . . . . . . . 16
|
21 | 17, 11 | atbase 34576 |
. . . . . . . . . . . . . . . 16
|
22 | 20, 21 | syl 17 |
. . . . . . . . . . . . . . 15
|
23 | | simp3r 1090 |
. . . . . . . . . . . . . . . 16
|
24 | 17, 10, 11 | hlatjcl 34653 |
. . . . . . . . . . . . . . . 16
|
25 | 7, 9, 23, 24 | syl3anc 1326 |
. . . . . . . . . . . . . . 15
|
26 | | ps1.l |
. . . . . . . . . . . . . . . 16
|
27 | 17, 26, 10 | latjle12 17062 |
. . . . . . . . . . . . . . 15
|
28 | 16, 19, 22, 25, 27 | syl13anc 1328 |
. . . . . . . . . . . . . 14
|
29 | | simpl 473 |
. . . . . . . . . . . . . 14
|
30 | 28, 29 | syl6bir 244 |
. . . . . . . . . . . . 13
|
31 | 30 | adantr 481 |
. . . . . . . . . . . 12
|
32 | | simpl1 1064 |
. . . . . . . . . . . . 13
|
33 | | simpl21 1139 |
. . . . . . . . . . . . 13
|
34 | | simpl3r 1117 |
. . . . . . . . . . . . 13
|
35 | | simpl3l 1116 |
. . . . . . . . . . . . 13
|
36 | | simpr 477 |
. . . . . . . . . . . . 13
|
37 | 26, 10, 11 | hlatexchb1 34679 |
. . . . . . . . . . . . 13
|
38 | 32, 33, 34, 35, 36, 37 | syl131anc 1339 |
. . . . . . . . . . . 12
|
39 | 31, 38 | sylibd 229 |
. . . . . . . . . . 11
|
40 | 39 | 3impia 1261 |
. . . . . . . . . 10
|
41 | 14, 40 | eqtrd 2656 |
. . . . . . . . 9
|
42 | 6, 41 | breqtrrd 4681 |
. . . . . . . 8
|
43 | 42 | 3expia 1267 |
. . . . . . 7
|
44 | 17, 10, 11 | hlatjcl 34653 |
. . . . . . . . . . 11
|
45 | 7, 8, 9, 44 | syl3anc 1326 |
. . . . . . . . . 10
|
46 | 17, 26, 10 | latjle12 17062 |
. . . . . . . . . 10
|
47 | 16, 19, 22, 45, 46 | syl13anc 1328 |
. . . . . . . . 9
|
48 | | simpr 477 |
. . . . . . . . . 10
|
49 | | simp23 1096 |
. . . . . . . . . . . 12
|
50 | 49 | necomd 2849 |
. . . . . . . . . . 11
|
51 | 26, 10, 11 | hlatexchb1 34679 |
. . . . . . . . . . 11
|
52 | 7, 20, 9, 8, 50, 51 | syl131anc 1339 |
. . . . . . . . . 10
|
53 | 48, 52 | syl5ib 234 |
. . . . . . . . 9
|
54 | 47, 53 | sylbird 250 |
. . . . . . . 8
|
55 | 54 | adantr 481 |
. . . . . . 7
|
56 | 43, 55 | syld 47 |
. . . . . 6
|
57 | 56 | 3impia 1261 |
. . . . 5
|
58 | 57, 41 | eqtrd 2656 |
. . . 4
|
59 | 58 | 3expia 1267 |
. . 3
|
60 | 17, 10, 11 | hlatjcl 34653 |
. . . . . . 7
|
61 | 7, 8, 23, 60 | syl3anc 1326 |
. . . . . 6
|
62 | 17, 26, 10 | latjle12 17062 |
. . . . . 6
|
63 | 16, 19, 22, 61, 62 | syl13anc 1328 |
. . . . 5
|
64 | | simpr 477 |
. . . . 5
|
65 | 63, 64 | syl6bir 244 |
. . . 4
|
66 | 26, 10, 11 | hlatexchb1 34679 |
. . . . 5
|
67 | 7, 20, 23, 8, 50, 66 | syl131anc 1339 |
. . . 4
|
68 | 65, 67 | sylibd 229 |
. . 3
|
69 | 5, 59, 68 | pm2.61ne 2879 |
. 2
|
70 | 17, 10, 11 | hlatjcl 34653 |
. . . . 5
|
71 | 7, 8, 20, 70 | syl3anc 1326 |
. . . 4
|
72 | 17, 26 | latref 17053 |
. . . 4
|
73 | 16, 71, 72 | syl2anc 693 |
. . 3
|
74 | | breq2 4657 |
. . 3
|
75 | 73, 74 | syl5ibcom 235 |
. 2
|
76 | 69, 75 | impbid 202 |
1
|